Chat with tutor

Ask Questions, Get Answers

Questions  >>  CBSE XI  >>  Math  >>  Conic Sections

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

$\begin {array} {1 1} (A)\;\large\frac{x^2}{25}-\large\frac{y^2}{9}=1 & \quad (B)\;\large\frac{x^2}{9}+\large\frac{y^2}{25}=1 \\ (C)\;\large\frac{y^2}{25}-\large\frac{x^2}{9}=1 & \quad (D)\;\large\frac{x^2}{25}+\large\frac{y^2}{9}=1 \end {array}$

1 Answer

  • Equation of an ellipse whose major axis is along the x - axis is given by $ \large\frac{x^2}{a^2}$$+\large\frac{y^2}{b^2}$$=1$
  • If a point move in a plane in such a way that the sum of its distances from two fixed points is constant, then the path is an ellipse . The constant value is equal to the length of the major axis of the ellipse.
Step 1 :
Let us take A and B as the two positions of the two flag posts and P be the position of the man.
$ \therefore PA + PB = 10$
Hence it is clear that the path described by the man is an ellipse.
The points A and B are the foci.
The length of the major axis is 10 m.
Step 2 :
The equation of the ellipse is of the form $\large\frac{x^2}{a^2}$$+\large\frac{y^2}{b^2}$$=1$
Since $2a=10 \Rightarrow a = 5$
Distance between the foci is 2c = 8
$ \therefore c = 4$
We know $c = \sqrt{a^2-b^2}$
or $ c^2 = a^2-b^2$
Substituting the value for c and a we get,
$16 = 25-b^2$
$ \therefore b^2=9 \Rightarrow b = 3$
Hence the equation of the path traced by the man is
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.